@inproceedings{94d980e1a7244fa5913f4f76b47dbb25,
title = "Classification of evolution equations possessing two-soliton solutions and lax pairs by direct methods",
abstract = "A direct method for constructing transformations from traveling wave solutions to non-traveling wave solutions of an evolution equation, has been developed. In the case, when applying the method yields transformations from one-soliton solutions to two-soliton solutions, it may be used for construction of the many-parameter families of evolution equations possessing two-soliton solutions. Such equations may, to some extent, be considered as candidates for integrable equations. In order to separate presumably integrable equations from those families, a direct method for identifying conditions for the Lax pair existence has been developed. Some new equations admitting the Lax pairs have been identified using the method.",
keywords = "Direct methods, Integrable equations, KdV type equations, Lax pairs, Solitons",
author = "Burde, {Georgy I.}",
note = "Publisher Copyright: {\textcopyright} 2015 AIP Publishing LLC.; International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014 ; Conference date: 22-09-2014 Through 28-09-2014",
year = "2015",
month = mar,
day = "10",
doi = "10.1063/1.4912649",
language = "English",
series = "AIP Conference Proceedings",
publisher = "American Institute of Physics Inc.",
editor = "Simos, {Theodore E.} and Simos, {Theodore E.} and Simos, {Theodore E.} and Charalambos Tsitouras",
booktitle = "Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014",
}